# Right Prism: Surface Area

How to find the surface area of a right prism: definition, formula, 2 examples, and their solutions.

## Prism

### Definition

A prism is a 3D figure
that has
a pair of polygon bases

The bases are congruent and parallel.

## Right Prism

### Definition

A right prism is a prism
whose lateral faces are all rectangles
and are perpendicular to the bases.

## Formula

### Formula

A = 2B + Ph

A: Surface area of a right prism
B: Base area
P: Perimeter of the base
h: Height

2B is the two base areas.
Ph is the lateral area.

## Example 1

### Solution

Find the base area B.

The base is a rectangle.
Its sides are 7 and 5.

So the area of the rectangle is
B = 7⋅5.

7⋅5 = 35

So the base area B is 35.

Find the perimeter of the base P.

The base is a rectangle.
So its sides are 7, 5, 7, and 5.

So the perimeter P is 2(7 + 5).

7 + 5 = 12

2⋅12 = 24

So the perimeter of the base P is 24.

The height h is 8.

B = 35
P = 24
h = 8

Then the surface area A
is equal to,
two base areas 2B, 2⋅35

plus,
the lateral area Ph, 24⋅8.

So A = 2⋅35 + 24⋅8.

2⋅35 = 70
+24⋅8 = +192

70 + 192 = 262

So the surface area of the right prism is
262.

## Example 2

### Solution

Find the base area B.

The base is an equilateral triangle.
Its side is 4.

So the area of the equilateral triangle is
B = [√3/4]⋅42.

[√3/4]⋅42
= √3⋅4
= 4√3

So the base area B is 4√3.

Find the perimeter of the base P.

The base is an equilateral triangle.
So its sides are 4, 4, and 4.

So the perimeter P is 3⋅4.

3⋅4 = 12

So the perimeter of the base P is 12.

The height h is 7.

B = 4√3
P = 12
h = 7

Then the surface area A
is equal to,
two base areas 2B, 2⋅4√3

plus,
the lateral area Ph, 12⋅7.

So A = 2⋅4√3 + 12⋅7.

2⋅4√3 = 8√3
+12⋅7 = +84

Arrange the terms.

So the surface area of the right prism is
84 + 8√3.